Question

A coil has 100 turns, each of area 0.05 m² and total resistance 1.5 Ω. It is inserted at an instant in a magnetic field of 90 mT, with its axis parallel to the field. The charge induced in the coil at that instant is ______.

विकल्प

• 3.0 mC

• 0.30 C

• 0.45 C

• 1.5 C

Answer 1

A coil has 100 turns, each of area 0.05 m² and total resistance 1.5 Ω. It is inserted at an instant in a magnetic field of 90 mT, with its axis parallel to the field. The charge induced in the coil at that instant is 0.30 C.

Explanation:

Given: Number of turns (N) = 100

Area of each turn (A) = 0.05 m²

Total resistance (R) = 1.5 Ω

Magnetic field (B) = 90 m T = 90 × 10⁻³ T

Initial flux (Φ_Bi) = BA = (90 × 10⁻³) × (0.05) = 4.5 × 10⁻³ Wb

Final flux (Φ_Bf) = 0 Wb

Change in flux (ΔΦ_B) = Φ_Bf − Φ_Bi = −4.5 × 10⁻³ Wb

Using Faraday’s Law:

e = `-N ((Delta phi_B)/(Delta t))`

Total charge induced:

Q = IΔt

= `(epsilon Delta t)/R`

= `-N (Delta phi_B)/R`

Substituting values:

Q = `((100) xx (-4.5 xx 10^-3))/1.5`

= `(-0.45)/1.5`

= −0.3 C